Issue 41

J.V. Sahadi et alii, Frattura ed Integrità Strutturale, 41 (2017) 106-113; DOI: 10.3221/IGF-ESIS.41.15 108 stress cases were run at lower peak stresses. It was observed that in most cases yielding occurred during the first cycle, but no “reversed yielding'' took place when load was removed. Hence subsequent load cycles at the same load level did not cause additional plastic deformation despite the material being loaded close to the elastic limit on each cycle. Such observation is very important as it set the ground for the multiaxial criteria candidates for fatigue life prediction. Exp. No. Load case Peak load [kN] Norm. Peak Strain Norm. Peak Stress Biaxiality Ratio Cycles Horizontal Vertical ε x ε y σ x σ y σ vM Load Strain Stress CX01 Single actuator 117 0 1.31 −0.71 1.21 −0.36 1.43 0 −0.54 −0.30 87,765 CX02 Equi-biaxial 170 170 0.88 0.88 1.23 1.23 1.23 1 1 1 65,426 CX03 Equi-biaxial 170 170 0.88 0.88 1.23 1.23 1.23 1 1 1 57,884 CX04 Single actuator 117 0 1.31 −0.71 1.21 −0.36 1.43 0 −0.54 −0.30 97,560 CX05 Pure shear 90 −90 1.56 −1.56 1.21 −1.21 2.1 −1.00 −1.00 −1.00 25,789 CX06 Pure shear, low ε 51 −51 0.88 −0.88 0.69 −0.69 1.19 −1.00 −1.00 −1.00 510,000 (Runout) CX07 Uniaxial Eq. 128.5 38.5 1.21 −0.34 1.21 0 1.21 0.3 −0.28 0 154,396 CX08 Min von Mises 147.8 102.8 1.04 0.26 1.21 0.61 1.05 0.7 0.25 0.5 107,004 CX09 Uniaxial Eq., low ε 93.6 28.1 0.88 −0.25 0.88 0 0.88 −1.00 −0.28 0 658,164 CX10 Pure shear, low σ 65.5 −65.5 1.13 −1.13 0.88 −0.88 1.53 −1.00 −1.00 −1.00 236,935 CX11 Pure shear 90 −90 1.56 −1.56 1.21 −1.21 2.1 −1.00 −1.00 −1.00 21,684 Table 1: Experimental tests parameters and results. A NALYSIS Stress-based criteria n introductory analysis of the test data was achieved by considering extensions of yield theories to multiaxial fatigue and stress based criteria. The formulations of von Mises, elastic strain energy equivalent stress, Crossland [9], Findley [10]and Matake [11] were investigated. Among them, the energy parameter and Crossland’s invariant based approach gave the best predictions. The elastic strain energy density is the sum of the products of strain and stress (divided by 2). In the case of plane stress and no shear, a uniaxial stress with equivalent strain energy to a biaxial stress state is formulated as:            U 2 2 2 2 e 1 2 1 2 2 (1) where  represents the Poisson's ratio. Fig. 2 (a) presents the correlation between this parameter normalized and the test data in cycles to failure. The stress-life curve was obtained using Basquin’s relation (power relationship) and using the equivalent stress presented in Eq. (1). The criterion presented good results with a coefficient of correlation, r 2 , of 0.868. Among all the test cases, the pure shear low stress case was the furthest to the trend line. In sequence, some of the most widely used stress based criteria were investigated. The stress invariant based criterion proposed by Crossland [9] considers the amplitude of the second invariant of the deviatoric stress tensor, J 2a (which corresponds to the amplitude of von Mises equivalent stress) and the maximum value of the first invariant of Cauchy’s A